Sunday, September 11, 2016

Circular Definitions, Arguments, and Explanations

In the course of our discursive operations we often encounter circularity. Clarity will be served if we distinguish different types of circularity. I count three types. We could label them definitional, argumentative, and explanatory.

A. The life of the mind often includes the framing of definitions. Now one constraint on a good definition is that it not be circular. A circular definition is one in which the term to be defined (the definiendum) or a cognate thereof occurs in the defining term (the definiens). 'A triangle is a plane figure having a triangular shape,' though plainly true, is circular. 'The extension of a term is the set of items to which the term applies' is an example of a non-circular definition.

B. Sometimes we argue. We attempt to support a proposition p by adducing other propositions as reasons for accepting p. Now one constraint on a good argument is that it not be circular. A circular argument in is one in which the conclusion appears among the premises, sometimes nakedly, other times clothed for decency's sake in different verbal dress. Supply your own examples.

C. Sometimes we explain. What is it for an individual x to exist? Suppose you say that for x to exist is for some property to be instantiated. One variation on this theme is to say that for Socrates to exist is for the haecceity property Socrateity to be instantiated. This counts as a metaphysical explanation, and a circular one to boot. For if Socrateity is instantiated, then it is is instantiated by Socrates who must exist to stand in the instantiation relation. The account moves in a circle, an explanatory circle of embarrassingly short diameter.

Suppose someone says that for x to exist is for x to be identical to something or other. They could mean this merely as an equivalence, in which case I have no objection. But if they are shooting for a explanation of existence in terms of identity-with-something-or-other, then they move in an explanatory circle. For if x exists in virtue of its identity with some y, then y must exist, and you have moved in an explanatory circle.

Some philosophers argue that philosophers ought not be in the business of explanation. I beg to differ. But that is a large metaphilosophical topic unto itself.